"RICHARD SEDGWICK, of England, came in 1806 and settled at Richmond, Indiana. He had two sons, John and Charles.
Isham and Richard Sedgwick were sons of John, and they were proprieters of Sedgwick Brothers,
manufacturers of fences and gates, at Richmond, Ind., for many years."

On January 13, 1808, Richard Sedgwick parts of Sections 10 and 11 of Range 1W Twp 12N.
The land east of the Greenville Treaty Line and west of the the present Indiana - Ohio border
was then part of Ohio Territory2.
The records of his purchase therefore appear with early Ohio land records.4
Beverly Yount says it was "a farm of 300 acres, three miles south of Boston, Harrison Twp, Union County, Indiana"3

A Richard Sedwick arrived at Philadelphia on April 20, 1807, aboard the Ship Halcyon, departed Liverpool.7
This might be this Richard.

In court proceedings held in Ross County, Ohio, on "4th Wednesday September 1799",
the jury included one Richard Sedwick. I wonder if this is the same Richard?

Charles Hunt of North Carolina and his wife Mary moved to Wayne County in 1807,
having sent ahead four sons to start work building the first grist-mill in the area
and daughter Sally to cook for them.6
Richard Sedgwick and Sarah (Sally) Hunt, daughter of Charles and Mary, were married in 1808.6,3,2

"The first Carding Machine--a rude establishment--was put up by Richard Sedgwick and Smith Hunt, at the mouth of Elkhorn."2 Smith Hunt was one of Sally's brothers.
A carding machine would be one that combs fibers with metal brushes or spikes to untangle them in preparation for spinning.

We see in 1930 that Richard had two sons and four daughters.
The sons names are given in the excerpt above.
I find marriage records for the sons in Wayne and Union Counties, and for four Sedgwick women in Union County in the 1830's and 1840's.
Since this appears to be the only Sedgwick family in the area at the time, I believe the four women to be the four daughters.

Pages for the rest of the children will be made as time permits;
meanwhile some of the data is collected here:

Agnes Sedgwick married Levi Druley January 17, 1833. They lived in Wayne County, Indiana and appear in the 1850 and 1880 censuses.

Mary Sedgwick married John P Smith on March 10, 1844. They appear in the 1850 Census in Union County and the 1880 Census in Wayne County. He was co-owner of the Charter Oak Pork House, a large slaughterhouse

Two of Richard's children, Mary and John, married descendants of Adam Schmeltzer (1724 - 1796), an immigrant to Pennsylvania.
Their descendants are delineated in the book Asters at Dusk, the Smeltser family in America

Sources and notes (all sources for this family listed here):

1. Census records, any of those indicated.

2. History of Wayne County Indiana
book, Andrew W Young, Cincinnati, Robert Clarke and Company, 1872
available at GenealogyLibrary.com
features a portrait of Mary Hunt, mother of Sarah (Sally) Hunt, on page 149